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$Drilling-induced tensile wall-fractures - Stanford University$

(CBs) and the matrix rock in all simulations (although these permeabilities are locally isotropic, large-scale anisotropy will result from the CB orientation). Equation (1) can be extended to accommodate two-phase flow by considering Darcy's law and mass conservation for each phase separately: ( φS ) ∂ ∂t ( φS ) ∂ ∂t ⎛ kk = ∇⋅ ⎜ ⎝ ∇ ⎞ ⎟ ⎠ n rn ⎜ pn ⎟ + Qn µ n ⎛ kk = ∇⋅ ⎜ ⎝ ∇ ⎞ ⎟ ⎠ w rw ⎜ pw ⎟ + Q w µ w , (2) , (3) where subscripts n and w refer to nonwetting and wetting phases. Saturation (phase volume fraction) S is defined for each phase. The porosity of the rock is designated byφ , and in addition to the absolute permeability , a relative permeability, k , is defined for k r each phase. A capillary pressure (pc) relationship expresses the difference in pressure between the two phases as a function of S; i.e., pc( Sw) = pn − pw . An additional constraint requires Sn + Sw = 1 . For all the flow scenarios, the governing equations are solved using a specialized finite-volume discretization technique, namely a discrete-feature model, developed by Karimi-Fard et al. (2004). Although originally designed to model flow in fractured porous media, where the discrete features provide high-permeability channels, the generality of the method allows low-permeability features such as CBs to be treated equally well. The technique is designed for use with unstructured grids (in both two and three dimensions), which can accurately represent complex natural geometries such as the CB map (Figure 7.3). A particular strength of the method is that it allows small-scale linear features such as CBs to be represented and modeled using control volumes that are of the same thickness as the feature, meaning that CBs need not be resolved in the transverse (thin) direction by the grid. This reduces the overall number of cells required and greatly simplifies the gridding procedure. In addition, inefficiencies caused by the proliferation of small control volumes at CB intersections are mitigated using a special connectivity transformation, which improves numerical stability and allows for larger time steps in transport problems in some cases (Karimi-Fard et al., 2004). 176
(c) (a) (b) l d lm A j m d m A j A j m b ll bb d lm l m Figure 7.4. Schematic diagrams depicting quantities relevant to the transmissibility calculations for (a) matrix to matrix flow, (b) matrix to compaction band flow and (c) compaction band to compaction band flow. The band thickness is exaggerated in (b) and (c). 177
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STRUCTURAL GEOLOGY, PROPAGATION MEC
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Abstract Low-porosity, low-permeabi
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delivered with fortitude, humor, su
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Chapter 3—Energy-release model of
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List of Illustrations Figure A. Cov
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Figure A. Cover photo that accompan
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likely present in subsurface sandst
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hooking-tip interactions—using th
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and sandstone, my co-authors—Moha
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the hard data from which accurate p
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Although the Aztec sandstone experi
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Waterpocket Fault 36 o 26‘ N 0 1
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Cenozoic Mesozoic Paleozoic Quatern
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3.3. Deformation The Aztec also has
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There also are relatively high-angl
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(e) (f) (c) 500µm compaction band
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dihedral angle of 80° or more, and
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5. Compaction band orientations Ori
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n = 20 M n = 20 P n = 22 B n = 20 R
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were encountered, giving the dihedr
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Eichhubl et al., 2004) did not lend
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P (a) (c) S P S Figure 1.10. Stereo
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possible, and use these to better c
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1.5(ρgz) (b) WEST Willow Tank Uppe
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9. Acknowledgements My sincere than
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The term compaction band (CB) was c
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Pollard, 2002). The particular util
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Hue-based image analysis using MATL
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a direct genetic relationship (Hill
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Compaction band fin Depositional be
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suggests—that to first approximat
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Porosity Porosity 0.3 0.25 0.2 0.15
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pore-clogging clay—due presumably
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500 µm Figure 2.9. Electron backsc
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(a) (b) σ 3 σ 1 x 3 x 1 x 1 (c) u
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6. Elastic properties Despite a lon
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Comparison of the two approaches es
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term in (6a) and (6c) begins to dom
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MPa MPa 80 70 60 50 40 30 20 10 0 0
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2002) and use a BEM approach (Crouc
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MPa 10 4 10 3 10 2 10 1 10 −5 10
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concentration of quartz plasticity
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conducted on well-cemented sandston
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~ 62 m compaction band trend 500µm
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Sternlof et al. (2005) have suggest
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2005). It consists of a long (infin
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⎡ ∆ ⎤ ⎧ p 1 ∆ ⎛ M ⎞
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which point the inelastic strain ha
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they can exert significant effects
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interact is inversely proportional
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(a) (b) (c) (d) Figure 4.3. Typical
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Viewed individually, CB traces tend
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(a) (b) (c) (d) (e) (f) Figure 4.7.
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1973; Mardon, 1988; Peck et al., 19
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undamaged host rock. That CBs canno
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0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2
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Normalized stress magnitude 3 2.5 2
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helps to explain why the oblique ap
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and ts = G·ds + H·dn (2) where tn
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plastic compaction, as suggested by
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To determine the sensitivity of pro
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segments will self-correct to provi
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6.3. Approaching tip interactions A
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0.2 0.15 0.1 0.05 0 −0.05 −0.1
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0.2 0.15 0.1 0.05 0 −0.05 −0.1
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the hooking patterns commonly obser
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(a) (b) (c) σ1 compaction band max
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σ 3 σ 2 σ 1 Figure 4.24. Schemat
Page 138 and 139: NV UT CA AZ Park Road Map Detail Pa
Page 140 and 141: compaction band Figure 5.2. Typical
Page 142 and 143: 3. Computational method The methodo
Page 144 and 145: compaction band A 5 mm A‘ compact
Page 146 and 147: 4. Application to the Aztec sandsto
Page 148 and 149: Permeability (mD) 10 4 10 3 10 2 10
Page 150 and 151: B‘ A‘ A c f m c m c f c f c f c
Page 152 and 153: equivalent of the Aztec sandstone,
Page 154 and 155: effective permeability represents a
Page 156 and 157: NV UT CA AZ Park Road Map Detail Pa
Page 158 and 159: Commonly from ~1 mm to ~1.5 cm in t
Page 160 and 161: Although systematic arrays of DBs p
Page 162 and 163: to 2 m, with both sets in a cross-h
Page 164 and 165: y identical blocks all subject to t
Page 166 and 167: contiguous areas. This type of char
Page 168 and 169: (0,b) n 3 (0,0) f 2 n 2 n 1 (a,0) (
Page 170 and 171: 6.1. Parallel Effective permeabilit
Page 172 and 173: By contrast, band-parallel effectiv
Page 174 and 175: Relative Effective Permeability 1.0
Page 176 and 177: (a) (b) (c) 0 meters 3 = 10-2 kb /k
Page 178 and 179: Though grossly systematic, anastomo
Page 180 and 181: 168
Page 182 and 183: 100 meters 5 meters NV UT CA AZ Par
Page 184 and 185: compaction band trend 500µm Figure
Page 186 and 187: Cover Outcrop Band N 100 meters 20
Page 190 and 191: The finite volume discretization fo
Page 192 and 193: isotropic) can lead to numerical di
Page 194 and 195: 5. Simulations Three sets of 2-D si
Page 196 and 197: Normalized ∆P ∆P ratio (n/p) 4.
Page 198 and 199: P P P P I I P P Case 1 P P Case 2 I
Page 200 and 201: Case 1 Case 1 Case 1 (a) (b) (c) In
Page 202 and 203: 5.2.2. Discussion The elliptical pa
Page 204 and 205: 5.3.1. Results With the regional gr
Page 206 and 207: (a) (b) Leak 200 meters Regional gr
Page 208 and 209: anticipated sustainable pumping rat
Page 210 and 211: Finally, there is the issue of fore
Page 212 and 213: 200
Page 214 and 215: Bakke, S., and Øren, P. E., 1997,
Page 216 and 217: Carpenter, D. G., and Carpenter, J.
Page 218 and 219: Eichhubl, P., Taylor, W. L., Pollar
Page 220 and 221: Karimi-Fard, M., Durlofsky, L. J.,
Page 222 and 223: -, 1987, Fracture from a straight c
Page 224 and 225: Shipton, Z. K., and Cowie, P. A., 2
Page 226: Wong, T. F., David, C., and Zhu, W.
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